2 Specification

3 Description

nag_dorghr (f08nfc) is intended to be used following a call to nag_dgehrd (f08nec), which reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: A=QHQT. nag_dgehrd (f08nec) represents the matrix Q as a product of ihi-ilo elementary reflectors. Here ilo and ihi are values determined by nag_dgebal (f08nhc) when balancing the matrix; if the matrix has not been balanced, ilo=1 and ihi=n.

This function may be used to generate Q explicitly as a square matrix. Q has the structure:

Q=I000Q22000I

where Q22 occupies rows and columns ilo to ihi.

4 References

5 Arguments

1:
order – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

9 Example

Here A is general and must first be reduced to Hessenberg form by nag_dgehrd (f08nec). The program then calls nag_dorghr (f08nfc) to form Q, and passes this matrix to nag_dhseqr (f08pec) which computes the Schur factorization of A.